What is the Vigenère Cipher?

The Vigenère cipher is a polyalphabetic substitution cipher that is a natural evolution of the Caesar cipher. The Caesar cipher encrypts by shifting each letter in the plaintext up or down a certain number of places in the alphabet. If the message was right shifted by 4, each A would become E, and each S would become W.

In the Vigenère cipher, a message is encrypted using a secret key, as well as an encryption table (called a Vigenere square, Vigenere table, or tabula recta). The tabula recta typically contains the 26 letters of the Latin alphabet from A to Z along the top of each column, and repeated along the left side at the beginning of each row. Each row of the square has the 26 letters of the Latin alphabet, shifted one position to the right in a cyclic way as the rows progress downwards. Once B moves to the front, A moves down to the end. This continues for the entire square.

Also, other alphabets than the English alphabet can be used in a similar way to construct a tabula recta.

Let's take this plaintext phrase as an example:

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After finalizing the plaintext, the person encrypting would then pick a secret key, which would help encrypt and decrypt the message. Our example secret key here is:

BOXENTRIQ

The next step is repeating the secret key enough times so its length matches the plain text.

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BOXENTR IQBO XENTRI QBOXENT RIQBOX

Once the two lines are split into five-letter groups, start encrypting. Take one letter from the plaintext group and a letter from the secret key group (we're going to start with I and B), and find the entry in the tabula recta where the row and column intersect. For this example, the first letter of the encrypted cipher text is J.

Once you've done that for every character, your final encrypted text should look like this:

JAMVB OVGEV FMYMS CMIPZ SMAZJ SYMZP

You can use this cipher for short or long messages. Once you've mastered the tabula recta, the encryption process is easy!

How to Decrypt it

If you have the secret key, decrypting is as easy as encrypting. You can work backwards using the tabula recta. First repeat the secret key so its length matches the cipher text.

JAMVB OVGEV FMYMS CMIPZ SMAZJ SYMZP

BOXEN TRIQB OXENT RIQBO XENTR IQBOX

Using the tabula recta, find the row that corresponds to the first letter in your secret key text- in our case, B. In the B row, find the corresponding cipher text letter J. The vertical column where that cipher text letter is located reveals the plaintext letter I.

The Vigenère cipher can also be described and then decrypted algebraically, by assigning each letter from A to Z a value from 0 to 25, with addition being performed modulo 26.

How to Break It

Of course, these decryption methods only work if the secret key is known. In his initial attack against the Vigenère cipher, Friedrich Kasiski had success by examining repeated strings of characters in the cipher text, which could indicate the length of the secret key. This method is now called the Kasiski examination. Finding more repeated strings of characters helps narrow down the length of the potential secret key. Once the length of the secret key is known, the cipher text is rewritten into a corresponding number of columns, with a column for each letter of the key. Each column is then made up of plaintext that's been encrypted by one Caesar cipher. The code-breaker then breaks the cipher text in a similar way to a Caesar cipher.

Auguste Kerckhoffs improved on Kasiski's method by matching each “column's letter frequencies to shifted plaintext frequencies to discover the key letter (Caesar shift) for that column.” Once the code-breaker knows each letter in the secret key, all they have to do is decrypt the cipher text using a Vigenere square.

Another option is the key elimination method. If you guess the key length and then subtract the ciphertext from itself, offset by the key length, it will eliminate the secret key. The result will be the plaintext subtracted from itself, offset by the key length. If any words longer than the key length can be guessed, their self-encryption can be searched for.

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